Debt underwriting and bond markets

Bond/debt underwriting includes the underwriting of: Government securities Corporate bonds Government bonds are typically risk free (except for foreign currency bonds), since governments have the right to print money Corporate bonds are not risk free 2

Role of investment banks INVESTORS Issuer: -Government -Company Underwriter 3

Pricing of risk free bonds Zero coupon bonds Has a single payout $M in n years time Call P the market price With M and P, we can calculate the current spot rate r for maturity date n: For a given M, the higher is r the lower the price P

Coupon paying bonds Provide a stream of coupons C The yield to maturity (YTM) y is such that: The YTM is a measure of the bond return

Yield to maturity If a bond sells for price P, has coupon amount C and face value M, with n years to maturity, the yield to maturity on the bond is the annual rate of interest you will receive if you buy the bond now for price P and hold it to maturity.

Extension to continuous compounding Often bonds pay coupons every 6 months For a n-year bond, there are 2n coupon payments The YTM is then such that:

YTM and coupon rate Call C/M the coupon rate If C/M=YTM, then P=M Bond sells at par If C/M<YTM, then P<M Bond sells at discount If C/M>YTM, then P>M Bond sells at premium

Pricing bonds using spot rates Reminder: the spot rate is the annual compound rate of return on an investment that has a payout at time n: Bonds can be viewed as a package of zero coupon bonds with different maturities, where each coupon is discounted at the appropriate spot rate:

Equilibrium prices are such that there is no arbitrage opportunity in the market Example: Consider a 2-year bond, with 4% annual coupon. The 1-year spot rate is 5%, and the 2-year spot rate is 6%. Calculate the market price.

British government securities Long-term bonds are called gilts Selected IB act as primary dealers Conventional stocks account for most of the market: Coupons are paid every 6 months, and there is a fixed payment at maturity Index linked stocks: Contrary to conventional stocks, the payments are adjusted to inflation, which provides a hedge against inflation

Imagine you have a £2bn and the following bids: At £99: for £1000m Pricing Imagine you have a £2bn and the following bids: At £99: for £1000m At £98 30/32: for £500m At £98 28/32: for £1000 Auction Tender £1000m sold at £99 £2000m sold at £98 30/32 £500m sold at £98 30/32 £500m sold at £98 28/32 with those who tendered above that price get the full amount tendered, and those who tendered at the price get 50%

Bid-to-cover ratio = ratio of bids received to the amount awarded. Tail of the auction = difference between the average yield of all accepted bids and the high yield. This signals the strength of the auction.

US treasury bonds Treasury securities are issued with maturity 2, 3, 5, 7, 10 and 30 years Treasury bills. Short-term securities with a maturity period of up to one year. They do not pay coupons. Holders receive the face amount at maturity. Treasury notes: Medium-term securities that have a maturity between 2 and 10 years. Treasury bonds: Long-term securities with maturity period of 30 years. They pay coupon every six months.

Price quotes in the UK The price is quoted per £100 of nominal stock in decimals. Example: a quote of 104.45 means a price of £104.45 for £100 nominal.

Price quotes in the US Price quotes are in units of 1/32 of 1% of par (where par is $100) Example of a quote: "6% Feb 26 at 99:07/99:09" refers to a 6% coupon bond redeemable in February 2026 with a bid-ask price of 99-7/32 and 99-9/32

Clean and dirty price The quoted price is called the clean price In reality, investors pay the "dirty price", which is more than the clean price due to the accrued interests When the buyer buys the bond between two coupon payments, he must compensate the seller for the interest for the coupon interest earned since the last coupon Accrued interest = C(n1/n2), where n1 is the number of days from the last coupon payment, and n2 is the number of days in the year

Cum-dividend bond sale The buyer receives the next coupon. Hence, the dirty price is the sum of the clean price and the accrued interest. Ex-dividend bond sale The next dividend payment goes to the seller. Hence, the dirty price is the clean price minus the rebate interest.